David Cameron speaks on welfare reform at Toynbee Hall in east London Photograph: Lewis Whyld/AP

Iain Duncan Smith's radical welfare bill, perhaps the most significant reshaping of the welfare state in 60 years, aims to simplify the system of subsidies that covers everything from income support to housing benefit to sickness payments.

For the government the aim is to remove the benefit traps that see some people lose 90p in every extra pound they earn as means-tested benefits are withdrawn. The new system will be paid for by deep cuts in welfare, as ministers push through savings of £18bn over the next four years.

There are signs of an unseemly rush to push through the bill, with details on a new child maintenance scheme published two months before a consultation on the issue is finished.

One of the most significant but little-heralded changes is that the welfare state should no longer be regarded as a piggy bank. In the past the public were told that by paying into national insurance, they would be guaranteed benefits should they fall on hard times.

Instead, the government will limit its new "employment and support allowance" to a year. This single reform saves more than £5bn.

But Citizens Advice chief executive Gillian Guy called it a "betrayal". "People who have worked hard and paid national insurance contributions [now] find that they do not get the support they need if they become sick or disabled before pension age."

Universal credit

A single "universal credit" will replace a panoply of welfare payments, while benefits to any one family will be capped at about £26,000. It is undoubtedly tough love. Lone parents with children aged five and older will be forced to seek work, losing benefits if they do not. Under universal credit, 2.7m households will receive higher payments and about 1.7m households will receive lower benefits.

Of the latter, more than 400,000 households will lose more than £25 a week – but the government says they will be compensated so "there are no losers". This, say some, creates a benefit trap, as few will want to take a job when they could see £1,300 a year in state aid disappear as a result.

Donald Hirsch, in a paper for the equality charity the Resolution Foundation, says single-earner couples will be far better off than poor double-income households. He calculates that the partner of a low-paid worker working 16 hours on the minimum wage would be £25 a week worse off under universal credit.

Given that such couples would need help with childcare, it is surprising that the government admits it has still not finalised the policy on "childcare payments and the method by which universal credit will be paid".

Welfare cap

The government is pushing ahead with attempts to drastically shrink the bill to the taxpayer. The first step is the cap on welfare payments. The government proposes that "total household welfare payments (of working age households)" be limited to £500 a week for couples and lone parent households, and to £350 a week for single person households. This will save the taxpayer £225m in 2013, the first year it is introduced. It will also see 50,000 households lose £93 a week – and the impact assessment accepts there will be a rise in homelessness: "Some households are likely to present as homeless, and may as a result need to move into more expensive temporary accommodation, at a cost to the local authority."

Housing benefit

Although the government has decided not to proceed with one measure – to cut the housing benefit of anyone on jobseeker's allowance by 10% – housing support is being pared back, with ministers saying that the £20bn annual cost to the taxpayer is too high.

About 1.4m households will lose out because benefits are being pegged to consumer prices (CPI) rather than the retail price index. This is in effect breaks the link between the housing costs people pay and the amount of housing support they receive. Shelter, the housing charity, says that as rents rise much faster than CPI, benefits will not be able to keep up with housing costs.

There is also a plan to cut an average of £13 from the housing benefit paid to 680,000 families living in social homes that could be considered "too big". Such families – often those with young children, people with disabilities or elderly people – will, if they cannot make up the shortfall, be compelled to move. Under the new rules, a separate bedroom is required only for each married or cohabiting couple, or any person aged over 21. Therefore, a couple with two adolescent sons would be penalised if they lived in a three-bedroom house.

Most of the families living in homes described as too large are in the north east and it is not clear where will they go. In addition, there is a national shortage of 240,000 one-bedroom properties. The National Housing Federation, which represents housing associations, says that although "ministers have long promised to protect the vulnerable … these plans could force thousands of people to move out of homes they have lived in for many years".

One of the most contentious proposals is the 20% cut to the disability living allowance (DLA), which at present pays a maximum of £70 a week in care costs and £50 in mobility bills. The government says the increase in claimants has become unsustainable. There are now 3.16 million people receiving DLA and forecast expenditure on the benefit for 2010-11 is £12.1bn. In eight years the number claiming DLA has risen from 2.4 million, an increase of 30%.

Although the main proposal remains on the table, the government says it will review plans to make £140m of savings by taking away state support for transport costs for disabled people living in state-funded care homes.

Universal Credit: Losers who loses?

Around 1.5m households keep more of the money they earn from working an extra hour. But more than 2m households will see their "marginal deduction rate" rise – and therefore have less incentive to work.

425,000

households will lose more than £25 a week, £1,300 a year.

100,000

will lose more than £75 a week, almost £4,000 a year.

330,000

second earners will lose more for each pound they earn under the proposals. More than half of those losing out under the scheme will be people working more than 30 hours a week; those receiving tax credits; and anyone not claiming housing benefit or council tax relief.